The statment $ \sim \left( {p \leftrightarrow  \sim q} \right)$ is

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

If $p, q, r$ are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true then

Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

The maximum number of compound propositions, out of $p \vee r \vee s , p \vee P \vee \sim s , p \vee \sim q \vee s$,

$\sim p \vee \sim r \vee s , \sim p \vee \sim r \vee \sim s , \sim p \vee q \vee \sim s$, $q \vee r \vee \sim s , q \vee \sim r \vee \sim s , \sim p \vee \sim q \vee \sim s$

that can be made simultaneously true by an assignment of the truth values to $p , q , r$ and $s$, is equal to

The proposition $p \Rightarrow \;\sim (p\; \wedge \sim \,q)$ is